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==Work Area==
−<pre>
−The word "intension" has recently come to be stressed in our discussions.
−As I first learned this word from my reading of Leibniz, I shall take it
−to be nothing more than a synonym for "property" or "quality", and shall
−probably always associate it with the primes factorization of integers,
−the analogy between having a factor and having a property being one of
−the most striking, at least to my neo-pythagorean compleated mystical
−sensitivities, that Leibniz ever posed, and of which certain facets
−of Peirce's work can be taken as a further polishing up, if one is
−of a mind to do so.
−As I dare not presume this to constitute the common acceptation
−of the term "intension", not without checking it out, at least,
−I will need to try and understand how others here understand
−the term and all of its various derivatives, thereby hoping
−to anticipate, that is to say, to evade or to intercept,
−a few of the brands of late-breaking misunderstandings
−that are so easy to find ourselves being surprised by,
−if one shies away from asking silly questions at the
−very first introduction of one of these parvenu words.
−I have been advised that it will probably be fruitless
−to ask direct questions of my informants in such a regard,
−but I do not see how else to catalyze the process of exposing
−the presumption that "it's just understood" when in fact it may
−be far from being so, and thus to clear the way for whatever real
−clarification might possibly be forthcoming, in the goodness of time.
−Just to be open, and patent, and completely above the metonymous board,
−I will lay out the paradigm that I myself bear in mind when I think about
−how I might place the locus and the sense of this term "intension", because
−I see the matter of where to lodge it in our logical logistic as being quite
−analogous to the issue of where to place those other i-words, namely, "idea",
−capitalized or not, "impresssion", "intelligible concept", and "interpretant".
−</pre>
To sum up, we have recognized the perfectly innocuous utility of admitting the abstract intermediate object <math>i,\!</math> that may be interpreted as an intension, a property, or a quality that is held in common by all of the initial objects <math>x_j\!</math> that are plurally denoted by the sign <math>y.\!</math> Further, it appears to be equally unexceptionable to allow the use of the sign <math>{}^{\backprime\backprime} i \, {}^{\prime\prime}</math> to denote this shared intension <math>i.\!</math> Finally, all of this flexibility arises from a universally available construction, a type of compositional factorization, common to the functional parts of the 2-adic components of any relation.
To sum up, we have recognized the perfectly innocuous utility of admitting the abstract intermediate object <math>i,\!</math> that may be interpreted as an intension, a property, or a quality that is held in common by all of the initial objects <math>x_j\!</math> that are plurally denoted by the sign <math>y.\!</math> Further, it appears to be equally unexceptionable to allow the use of the sign <math>{}^{\backprime\backprime} i \, {}^{\prime\prime}</math> to denote this shared intension <math>i.\!</math> Finally, all of this flexibility arises from a universally available construction, a type of compositional factorization, common to the functional parts of the 2-adic components of any relation.
−==Document History==
==Document History==
